基于分数Zener模型的植物油纸绝缘状态评估

Study on condition evaluation of vegetable oil-paper insulation based on fractional Zener model

介电响应理论的频域介电谱法可以有效地判断变压器的绝缘状况,因此为了量化研究植物油纸绝缘老化与频域介电谱的关系,本文引入分数元和分数微积分概念,提出了采用分数Zener模型提取植物油纸绝缘频域介电谱特征量的辨识方法。该方法能直接反映出油纸绝缘频域介电谱携带的信息,利用实验获取的复介电常数值求取分数Zener模型参数,即采用最小二乘法建立优化目标函数,并运用遗传算法求解模型参数,同时利用粒子群算法对其进行验证,得到特征量:形状参数β、参数εb、松弛时间τ,最后对计算结果重构。研究结果表明仿真结果与测量数据具有一致性,且低频段拟合度更高,建立的模型是可行的;得到的形状参数β、松弛时间τ与油中酸值呈指数函数关系,参数εb与油中酸值呈线性关系,因此,为评估植物油纸绝缘系统绝缘状态提供了一种新思路。

The frequency domain spectroscopy method of dielectric response theory can effectively assess the insulation condition of transformers.Therefore,in order to quantitatively study the relationship between aging of vegetable oil-paper insulation and frequency domain spectrum,the fractional Zener model is used to extract the characteristic quantities of the frequency domain spectrum of vegetable oil-paper insulation,with the concept of fractional element and fractional calculus introduced in this paper.This method can directly reflect the information carried by the frequency domain spectrum of oil-paper insulation,and obtain the parameters of fractional Zener model by using the complex permittivity obtained by the experiment.Firstly,the least square method is used to establish the optimization objective function.Then,the model parameters are obtained by using genetic algorithm,which contain the shape parameterβ,parameterεb and relaxation timeτ.The results are verified by particle swarm optimization algorithm.Finally,the calculation results are reconstructed.The results show that the simulation results are in good agreement with the measured data and the R-squared in low frequency is higher,which shows the suitability of this model.It is proved that the relation between shape parameterβ,relaxation timeτand acid value in the oil is exponential.The parameterεb has a linear relationship with the acid value in the oil.Therefore,a new idea for evaluating the insulation state of vegetable oil-paper insulation systems is provided.